402 research outputs found
Simple Algorithm for Factorized Dynamics of g_n-Automaton
We present an elementary algorithm for the dynamics of recently introduced
soliton cellular automata associated with quantum affine algebra U_q(g_n) at
q=0. For g_n = A^{(1)}_n, the rule reproduces the ball-moving algorithm in
Takahashi-Satsuma's box-ball system. For non-exceptional g_n other than
A^{(1)}_n, it is described as a motion of particles and anti-particles which
undergo pair-annihilation and creation through a neutral bound state. The
algorithm is formulated without using representation theory nor crystal basis
theory.Comment: LaTex2e 9 pages, no figure. For proceedings of SIDE IV conferenc
Scattering Rule in Soliton Cellular Automaton associated with Crystal Base of
In terms of the crystal base of a quantum affine algebra ,
we study a soliton cellular automaton (SCA) associated with the exceptional
affine Lie algebra . The solitons therein are labeled
by the crystals of quantum affine algebra . The scatteing rule
is identified with the combinatorial matrix for -crystals.
Remarkably, the phase shifts in our SCA are given by {\em 3-times} of those in
the well-known box-ball system.Comment: 25 page
Crystal Interpretation of Kerov-Kirillov-Reshetikhin Bijection II. Proof for sl_n Case
In proving the Fermionic formulae, combinatorial bijection called the
Kerov--Kirillov--Reshetikhin (KKR) bijection plays the central role. It is a
bijection between the set of highest paths and the set of rigged
configurations. In this paper, we give a proof of crystal theoretic
reformulation of the KKR bijection. It is the main claim of Part I
(math.QA/0601630) written by A. Kuniba, M. Okado, T. Takagi, Y. Yamada, and the
author. The proof is given by introducing a structure of affine combinatorial
matrices on rigged configurations.Comment: 45 pages, version for publication. Introduction revised, more
explanations added to the main tex
Factorization, reduction and embedding in integrable cellular automata
Factorized dynamics in soliton cellular automata with quantum group symmetry
is identified with a motion of particles and anti-particles exhibiting pair
creation and annihilation. An embedding scheme is presented showing that the
D^{(1)}_n-automaton contains, as certain subsectors, the box-ball systems and
all the other automata associated with the crystal bases of non-exceptional
affine Lie algebras. The results extend the earlier ones to higher
representations by a certain reduction and to a wider class of boundary
conditions.Comment: LaTeX2e, 20 page
Syntheses of some 1-(alpha-hydroxybenzyl)thieno[3,4-b]indolizine derivatives and their unexpected condensation reactions
Some ethyl 3-(benzyl or methylthio)-1-(alpha-hydroxybenzyl)- thieno[3,4-b]indolizine-9-carboxylates were prepared by the reduction of the corresponding 1-benzoyl derivatives with sodium borohydride. These compounds were considerably unstable and their treatment with acetic acid afforded the unexpected condensation products.ArticleHETEROCYCLES. 65(7): 1557-1560 (2005)journal articl
Box ball system associated with antisymmetric tensor crystals
A new box ball system associated with an antisymmetric tensor crystal of the
quantum affine algebra of type A is considered. This includes the so-called
colored box ball system with capacity 1 as the simplest case. Infinite number
of conserved quantities are constructed and the scattering rule of two olitons
are given explicitly.Comment: 15 page
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